The concept you mentioned, "heat has mass," is not accurate. Heat itself is not a substance or a form of matter that has mass. Heat is actually the transfer of energy from one object to another due to a temperature difference.
When you say "water has more mass than ice," you are referring to the fact that water in its liquid state is denser than ice in its solid state. This is due to the difference in the arrangement of water molecules in the two phases.
Regarding your question about the working mechanisms and how heat behaves at different temperatures, it is important to understand that temperature is a measure of the average kinetic energy of the particles in a substance. When heat is added to a substance, it increases the kinetic energy of the particles, leading to an increase in temperature.
The behavior of heat at different temperatures can be described using the laws of thermodynamics, particularly the specific heat capacity and the heat transfer mechanisms. Specific heat capacity is the amount of heat energy required to raise the temperature of a given mass of a substance by a certain amount. Different substances have different specific heat capacities, meaning they require different amounts of heat energy to produce the same temperature change.
Heat transfer mechanisms can be categorized into three types: conduction, convection, and radiation. Conduction is the transfer of heat through direct contact between objects or particles. Convection is the transfer of heat through the movement of a fluid (liquid or gas). Radiation is the transfer of heat through electromagnetic waves.
Regarding the application of these concepts in mathematics, there are mathematical equations and formulas that describe heat transfer, such as Fourier's Law for conduction and Newton's Law of Cooling for convective heat transfer. These equations allow us to mathematically model and analyze heat transfer processes in various systems.
However, it is important to note that heat itself is not a substance with mass. It is the transfer of energy. So, while mathematical models and equations can be used to describe heat transfer phenomena, the concept of heat having mass is not valid.